Abstract
© 2016, Springer-Verlag Berlin Heidelberg.Let (T2, g) be a Riemannian two-torus and let σ be an oscillating 2-form on T2. We show that for almost every small positive number k the magnetic flow of the pair (g, σ) has infinitely many periodic orbits with energy k. This result complements the analogous statement for closed surfaces of genus at least 2 (Asselle and Benedetti in Calc Var Partial Differ Equ 54(2):1525–1545. doi:10.1007/s00526-015-0834-1, 2015) and at the same time extends the main theorem of Abbondandolo et al. (J Eur Math Soc, arXiv:1404.7641, to appear) to the non-exact oscillating case.
| Original language | English |
|---|---|
| Pages (from-to) | 843-859 |
| Journal | Mathematische Zeitschrift |
| Volume | 286 |
| Issue number | 3-4 |
| DOIs | |
| Publication status | Published - 1 Aug 2017 |
| Externally published | Yes |
Funding
Luca Asselle is partially supported by the DFG Grant AB 360/2-1 “Periodic orbits of conservative systems below the Mañé critical energy value”. Gabriele Benedetti is partially supported by the DFG Grant SFB 878.
| Funders | Funder number |
|---|---|
| Deutsche Forschungsgemeinschaft | SFB 878, AB 360/2-1 |